Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution

Volume 16, Issue 3, pp 180--197 http://dx.doi.org/10.22436/jnsa.016.03.04

Publication Date: October 08, 2023 Submission Date: July 31, 2023 Revision Date: August 17, 2023 Accteptance Date: August 20, 2023

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Authors

B. Khan - School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, Peoples Republic of China. M. Ghaffar Khan - Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan. T. G. Shaba - Department of Mathematics, Landmark University, Omu-Aran 251103, Nigeria.

Abstract

In recent years, many new subclasses of analytic and bi-univalent functions have been studied and examined from different viewpoints and prospectives. In this article, we introduce new subclass of analytic and bi-univalent functions based on Mittag-Leffler type Borel distribution associated with the Gegenbauer polynomials. Furthermore we obtain estimates for \(\left\vert a_{2}\right\vert ,\) \(\left\vert a_{3}\right\vert \), and \(\left\vert a_{4}\right\vert \) coefficients and Fekete-Szego inequality for this functions class. Providing specific values to parameters involved in our main results, we get some new results.

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Keywords

• Analytic function
• bi-univalent function
• Gegenbaure polynomials
• coefficient estimates
• subordination
• Fekete-Szego functional problems

MSC

•  30C45
•  30C50
•  30C80

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